Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
688 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 688 conjugacy classes of subgroups — too many to draw. Only its 173 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #27132563 | C2 | semidirect |
| 3. #27132557 | C2 | semidirect |
| 4. #27132551 | C2 | semidirect |
| 5. #27132539 | C2 | semidirect |
| 6. #27132519 | C2 | semidirect |
| 7. #379×C191 | C2 | semidirect |
| 9. C22×C4×D191 | C22 | semidirect |
| 10. #20259291 | C4 | semidirect |
| 11. C2×Dic191⋊C4 | C22 | semidirect |
| 15. C2×(C2×D191)⋊C4 | C22 | semidirect |
| 16. C2×C4×Dic191 | C22 | semidirect |
| 17. C191⋊#95 | C22 | semidirect |
| 18. C191⋊#95 | C22 | semidirect |
| 33. C22⋊Dic191 | C2×C4 | semidirect |
| 38. C24×C191 | C2×C4 | semidirect |
| 95. C191 | #2375 | semidirect |
| 103. #379 | D191 | semidirect |
| 121. C24 | C4×D191 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20259291 | 2 |
| #27132563 | 2 |
| #27132557 | 2 |
| #27132551 | 2 |
| #27132539 | 2 |
| #27132519 | 2 |
| #379×C191 | 2 |
| #2375 | 191 |